The diagonals of a parallelogram bisect each other.

True

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False

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Solution

The correct option is A
True

The diagonals of a parallelogram bisect each other.

Given - $A B C D$ is a parallelogram.
To prove - $A E = E D$ and $B E = E C$
Proof -
In $△$ $E C D$ and $△$ $E B A$
$∠$ $E C D$ = $∠$ $E B A$ (alternate interior angles )
$∠$ $E D C$ = $∠$ $E A B$ (alternate interior angles )
$A B$ = $C D$ (Opposite sides of a parallelogram are equal)
$∴$ $△$ $E C D$ $≅$ $△$ $E B A$ ( by ASA congruency)
$∴$ $A E = E D$ and $B E = E C$ (c.p.c.t)

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Prove logically the diagonals of a parallelogram bisect each other. Show conversely that a quadrilateral in which diagonals bisect each other is a parallelogram.

Which of the given statements is incorrect

1.Diagonals of the parallelogram bisect each other.
2.If the Diagonals of a quadrilateral bisect each other,it is a parallelogram.
3.Diagonals of a parallelogram are equal.
4.Diagonals of the parallelogram are perpendicular to each other

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